What is the answer to log_{x+2}(3x^2+4x-14)=2 ?

The answer to log_{x+2}(3x^2+4x-14)=2 is x=3

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log_{x+2}(3x^2+4x-14)=2

lo g_{x + 2} (3 x^{2} + 4 x - 14) = 2

x = 3

Solution steps

lo g_{x + 2} (3 x^{2} + 4 x - 14) = 2

Apply log rules

\frac{ln ( 3 x ^{2} + 4 x - 14 )}{ln ( x + 2 )} = 2

Multiply both sides by

ln (x + 2)

\frac{ln ( 3 x ^{2} + 4 x - 14 )}{ln ( x + 2 )} ln (x + 2) = 2 ln (x + 2)

Simplify

ln (3 x^{2} + 4 x - 14) = 2 ln (x + 2)

Apply log rules

3 x^{2} + 4 x - 14 = (x + 2)^{2}

Solve

3 x^{2} + 4 x - 14 = (x + 2)^{2} : x = 3, x = - 3

x = 3, x = - 3

Verify Solutions:

x = 3

True

, x = - 3

False

The solution is

x = 3

ln (x^{2}) = 11

lo g_{2} (5 - x) - lo g_{2} (3 - x) = 2

lo g_{2} (x + 3) - lo g_{2} (x - 1) = 1

lo g_{8} (x) = 1.5

lo g_{3} (5) + lo g_{3} (8 + 3 x) = 5

What is the answer to log_{x+2}(3x^2+4x-14)=2 ?
The answer to log_{x+2}(3x^2+4x-14)=2 is x=3
Solve for x: log_{x+2}(3x^2+4x-14)=2
The solution is x=3